Experimental Analysis of BRDF Models

1
Experimental Analysis of BRDF Models

• Addy Ngan1 Frédo Durand1 Wojciech Matusik2
• MIT CSAIL1 MERL2

Eurographics Symposium on Rendering 2005
2
Goal

• Evaluate the performance of analytical
  reflectance models
• Based on measured data

3
Background

• Bidirectional Reflectance Distribution Function

4
BRDF

• Bidirectional Reflectance Distribution Function
• ?(?i ,?i ?o, ?o)

5
BRDF

• Bidirectional Reflectance Distribution Function
• ?(?i ,?i ?o, ?o)
• Isotropic material
• Invariant when material is rotated
• BRDF is 3D

6
Previous Measurements

• Columbia-Utrecht Reflectance and Texture Database
• 60 materials, 205 measurements per BRDF
• Cornells measurements
• 10 materials, 1439 measurements per BRDF
• Bonn BTF Database
• 6 materials, 6561 view/light combinations
• Matusiks image-based measurements
• 100 materials, 106 measurements per BRDF
• Include metals, plastic, paints, fabrics.

7
BRDF Models

• Phenomenological
• Phong 75
• Blinn-Phong 77
• Ward 92
• Lafortune et al. 97
• Ashikhmin et al. 00
• Physical
• Cook-Torrance 81
• He et al. 91

Lafortune 97
Cook-Torrance 81
8
Outline

• Background
• BRDF Measurements
• BRDF Fitting
• Isotropic materials results
• Anisotropic materials results
• Conclusion

9
BRDF Measurements

• Isotropic Data from Matusik 03
• 100 materials chosen
• Reprocessed to remove unreliable data
• Flare
• Near grazing angle
• Anisotropic New acquisition

10
Anisotropic Measurements

• Similar to Lu et al. 00

11
Anisotropic Measurements

• 4 materials measured (brushed aluminum, satins,
  velvet)
• Each 18 hours acquisition time, 30GB raw data
• Tabulated into bins in 2 intervals (108 bins)
• 10-20 bins populated

12
Outline

• Background
• BRDF Measurements
• BRDF Fitting
• Isotropic materials results
• Anisotropic materials results
• Conclusion

13
BRDF Fitting

• Target models Blinn-Phong, Cook-Torrance, He et
  al., Lafortune et al. , Ward, Ashikhmin-Shirley
• Metric
• RMS of (?measured M(p)) (cos ?i)
• Linear w.r.t. diffuse/specular intensity

14
BRDF Fitting

• Other potential metrics
• Logarithmic remapping
• Arbitrary scale
• Highlights overly blurry
• Perceptual metrics
• Context dependent
• Costly to compute/fit
• Intensity parameters become nonlinear
  optimization less stable

15
Outline

• Background
• BRDF Measurements
• BRDF Fitting
• Isotropic materials results
• Anisotropic materials results
• Conclusion

16
Fitting Errors
17
Dark blue paint
Acquired data
Environment map
Material Dark blue paint
18
Dark blue paint
Acquired data
Cook-Torrance
Material Dark blue paint
19
Dark blue paint
Acquired data
Blinn-Phong
Material Dark blue paint
20
Dark blue paint
Acquired data
Ward
Material Dark blue paint
21
Dark blue paint
Acquired data
Lafortune
Material Dark blue paint
22
Dark blue paint error plots
Lafortune
Ward
Cook-Torrance
Blinn-Phong
23
Dark blue paint

• Cook-Torrance fit, incidence plane, 4 different
  incident angles

Material Dark blue paint
24
Dark blue paint
Cook-Torrance
Material Dark blue paint
25
Dark blue paint
Original
Cook-Torrance
Lafortune
Ashikhmin
Material Dark blue paint
26
Lafortune Lobe

• Distorted highlights near grazing angle

Acquired data gold paint
Lafortune fit
27
Lafortune Lobe

• Distorted highlights near grazing angle

Acquired data nickel
Lafortune fit
28
Lobe Comparison

• Half vector lobe
• Gradually narrower when approaching grazing
• Mirror lobe
• Always circular

Half vector lobe
Mirror lobe
29
Half vector lobe

• Consistent with what we observe in the dataset.
• More details in the paper

Example Plot of PVC BRDF at 55 incidence
30
Observations - numerical

• Rough order of quality
• He, Cook-Torrance, Ashikhmin
• Lafortune
• Ward
• Blinn-Phong

Good fit
Poor fit
31
Observations - visual

• Mirror-like
• metals, some plastics
• All models match well visually
• Glossy
• paints, some metals, some wood
• Fresnel effect
• Distorted shape for Lafortune highlight
• Near diffuse
• fabrics, paints
• Fresnel effect

32
Observations

• Some materials impossible to represent with a
  single lobe

Acquired data
Cook-Torrance
Material Red Christmas Ball
33
Adding a second lobe

• Some materials impossible to represent with a
  single lobe

Acquired data
Cook-Torrance 2 lobes
Material Red Christmas Ball
34
Outline

• Background
• BRDF Measurements
• BRDF Fitting
• Isotropic materials results
• Anisotropic materials results
• Conclusion

35
Anisotropic Materials
36
Brushed Aluminum

• Reasonable qualitative fit

Acquired data
Ward
37
Yellow Satin

• Reasonable qualitative fit

Acquired data
Ward
38
Purple Satin

• Split highlights

?
39
Outline

• Background
• BRDF Measurements
• BRDF Fitting
• Isotropic materials results
• Anisotropic materials results
• Estimation of microfacet distribution
• Conclusion

40
Microfacet Theory

• Torrance Sparrow 1967
• Surface modeled by tiny mirrors
• Value of BRDF at
• of mirrors oriented halfway between L and
• Modulated by Fresnel, shadowing/masking

Shirley 97
41
Estimating the MF distribution

• Ashikhmins microfacet-based BRDF generator 00

42
Estimating the MF distribution

• Rearranging terms

43
Estimating the MF distribution
Measurements

• depends on the distribution
• Iterate to solve for
• Compute using current estimate
• Estimate given
• Converges quickly in practice

44
Purple Satin

• Split specular reflection

microfacet distribution
45
Purple Satin
Acquired data
microfacet distribution fit
46
Brushed Aluminum
Acquired data
microfacet distribution fit
47
Brushed Aluminum
microfacet distribution fit
Ward fit
48
MF-based BRDF generator

• Expressive
• Easy to estimate
• No optimization necessary
• Inexpensive to compute

49
Outline

• Background
• BRDF Measurements
• BRDF Fitting
• Isotropic materials results
• Anisotropic materials results
• Conclusion

50
Conclusion

• Isotropic materials
• He, Cook-Torrance, Ashikhmin perform well
• Explicit Fresnel
• multiple lobes help
• Half-vector based lobe performs better
• Most materials can be well-represented
• Anisotropic materials
• Cases where analytical models cannot match
  qualitatively
• Estimation of the microfacet distribution is
  straightforward
• Ashikhmins MF-based BRDF generator does well

51
Future Work

• Metric
• Generalized lobe based on half vector
• Efficient acquisition based on the microfacet
  distribution

52
Acknowledgement

• Eric Chan, Jan Kautz, Jaakko Lehtinen, Daniel
  Vlasic
• NSF CAREER award 0447561
• NSF CISE Research Infrastructure Award
  (EIA9802220)
• Singapore-MIT Alliance

53
Questions?